Sentence examples for be a closed separable from inspiring English sources

Let be a closed separable subset of a complete metric space, and let be measurable in and enjoy.

Let be a closed separable subset of a complete metric space, and let be a continuous hemicompact random operator.

Let H − be a closed separable subspace of a Hilbert space H with the norm ∥ ⋅ ∥ H and let H + : = ( H − ) ⊥.

Let be a closed separable subset of a complete metric space, and let be a lower semi-continuous random operator, which enjoys.

Let C be a closed separable subset of a complete metric space X, and let T : Ω × C → C ( X ) be a continuous hemicompact random operator.

Corollary 4.1 Let ( Ω, F ) be a measurable space, C be a closed separable subset of a complete metric space and let T : Ω × C → 2 X be a random operator which enjoys conditions ( P ) and α.

Let Y be a closed subspace of a separable Hilbert space X endowed with the inner product and the associated norm ∥ ⋅ ∥.

Let (Xin operatorname{AR}) be a closed subset of a separable Banach space E and let (varphicolonOmegatimes Xmultimap X) be a random u-operator with (R_{delta} -values such that (vaR_{delta} -values Xmultimap X) isuchmpacthator evarphi_{omega}colon.

Let ((Omega, {mathcal {F}})) be a measurable space, C be a closed, convex, bounded subset of a separable vector Banach space, and (F: Omegatimes Cto C) be a continuous condensing random operator.

Let F be a closed and convex subset of a separable Banach space X and the random iteration scheme {ξ t } defined as in Definition 2.2 is pointwise convergent, that is, ξ t → q := ξ for each ω ∈ Ω.

Let F be a closed and convex subset of a complete separable metric space X, and T: Ω × F → F be a weakly contractive random operator.